The relics of disrupted satellite galaxies have been found around the Milky Way and Andromeda, but direct evidence of a satellite galaxy in the early stages of disruption has remained elusive. We have discovered a dwarf satellite galaxy in the process of being torn apart by gravitational tidal forces as it merges with a larger galaxy's dark matter halo. Our results illustrate the morphological transformation of dwarf galaxies by tidal interaction and the continued buildup of galaxy halos.